Resumen de On the Symmetric Central Configurations of Three Coorbital Satellites

Jian Chen, Mingfang Yang, Peng Yang, Liping Zeng, Nan Yao

• We study the symmetric central configurations of the (1+3)-body problem, where three bodies (called satellites) are infinitesimal and the remaining one body is dominant.

  For this problem, in 2011, Corbera et al. (Celest Mech Dyn Astron 109:27–43, 2011) obtained the bifurcation value of mass parameter at which the number of central configurations changes by variables substitution and resultant theory. In this work, by qualitative analysis, we prove the sufficient and necessary conditions for producing the bifurcation value of mass parameter and figure out this value. Furthermore, we prove in detail why and how the number of central configurations changes when the mass parameter changes.